Deadcow has it right about nair > shine. I usually use it for priority reasons, too. For example, approaching with nairs do well against a character like. Captain Falcon because it outprioritizes all of C. Falcs aerials, including his nair, so you can definitely challenge his attack with one of your own and start a combo.
Shine > Usmash definitely works, but if your opponent is at the percentage where you can do it, you probably you have better options that wilol do more damage. Shine > dair > shine > dair > utilt > upair, etc. I definitely use upsmashes to end comboes on occasion though.
Shffled upairs work well when your opponent is on a platform. I've found that a lot of times it will shieldstab when you're underneath them, and it can also just be used to keep an opponent up in the air. Also it obviously has more vertical range than, say, a bair, so you're probably more likely to hit with it if you're coming from below.
There definitely are differences. Fox, Falco, C Falc, etc. are really easy to shine combo, and you'll probably use the types of shine combos you already know. Samus, on the other hand, is not as easy because of her floatiness. At low percentage, you might be able to get shine > dair > utilt > some other aerial, but that's about it. I actually like to use upairs against Samus to deal damage and try to keep her in the air, because her dair is not easy to hit with when coming down and if you're good enough you can sometimes hit two or more before she touches the ground.
IC's are definitely a different matchup that requires some experience to know well. You're coming down on two shields with your aerial, and thus the L-cancel timing is different, and you definitely should so that you don't get shieldgrabbed because IC grab = ****. You should definitely kill Nana whenever you can, or at least keep them separated, because one IC is a lot easier to deal with. If you can get an easy gimp on Nana, by all means go for it, even it means you might get grabbed by Popo, because a dead Nana is worth a little extra damage, especially if it's near the beginning of the IC's stock.
Against the IC's - Do not get grabbed. The IC's main combo starters are the Dthrow and dash attack. As long as you L-cancel properly and weave in and out of their range controlling the stage with lasers, you should do well. As a Falco player in general, and definitely agianst the IC's, it would be useful to learn how to ledgetech as well, because when you're recovering from below you will get smashed by the IC's, and in many cases their edgegurard moves are techable, allowing you to survive longer. And most people know that you cannot grab the IC's because the other one will just dsmash you, but Falco can. If you grab one of them, don't jab them at all but immediately dthrow. The lasers from the throw will hit both of them and the other IC won't be able to attack you., If you grabbed Nana, you can follow it up with a shine, dmash, dtilt, or whatever because she won't tech it.
